What is the location of the image of P(−8, 1) after a counterclockwise rotation of 90° about (−2, 6) ?
Answers
Answer:
(3, 0)
Step-by-step explanation:
Given:
Image: P = (-8, 1)Center of rotation: (-2, 6)Rotation rule for -90°: (x, y) → (y, -x)
As the center of rotation is not the origin, we cannot simply apply the above rule.
To rotate an image around a point other than the origin:
1. Subtract each point of the image from the point of rotation:
⇒ Point of rotation - point of image
⇒ (-2, 6) - P = (-2, 6) - (-8, 1)
= (6, 5)
2. Rotate this about the origin by applying the rotation rule:
⇒ (x, y) → (y, -x)
⇒ (6, 5) → (5, -6)
Add the point of rotation to each rotated point of the image:
⇒ (5, -6) + (-2, 6) = (3, 0)
Therefore, the location of the image of P (-8, 1) after a counterclockwise rotation of 90° about (-2, 6) is (3, 0).
Related Questions
if f(x)= 2x+1 and g(x)=x^2-2, what is (fig)(x)
Answers
2x+1 - (x^2-7)=2x+1-x^2+7 => -x^2+2x+8
the answer is C
Does anyone know how to do this
Answers
then you need to use simple algebra to left the x alone in the equation so you need to multiply both sides by 2 so you get
2y=10+x
then you need to subtract both sides a 10 so
2y-10=x
now change the x to f'(x) and y to x so:
f'(x)=2x-10
Raheem's rollerblades cost $70.25 less than his bicycle. His rollerblades cost $43.50. how much did his bicycle (B) cost?
Answers
Answer:
$113.75
Step-by-step explanation:
First add 70.25 to 43.50 to get 113.75
Answer:
$113.75
Step-by-step explanation:
b-70.25=43.50
add 70.25 to each side ..
b-70.25=43.50
+70.25+70.25
simpilfy...b=113.75
Which equation is correct?
O a
52 x 7 = 50+ 2 × 7
Ob
b
52 x 7 = 50 x 7+2
Oc
52 x 7 = 50 x 7+2x7
Od
52 x 7 = 500 ×7+2×7
Answers
Answer:
52 x 7= 50 x 7 + 2 x 7
Step-by-step explanation:
What is the angle relationship between ZBAC and ZDCA?
F
R
G
Answers
The angle BAC and DCA are alternate interior angles , Option D is the right answer.
What are Parallel Lines ?
The lines in a plane which never intersect and are at a same distance always are called Parallel Lines.
In the given question it is given that there are two lines FG and DE
The lines are parallel to each other , and transversal are AC and BC .
The angle BAC and DCA are alternate interior angles as AC is the transversal of the parallel lines.
Option D is the right answer.
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1. Solve the following simultaneous equations using the matrix method.
(a) LetA=(4 −3)
(2 5)
(i) Determine the determinant of A
(ii) Determine the adjoint of A
(iii) Determine the inverse of A
(iv) Hence, using the matrix method solve the following simultaneous
equations
4 − 3 = 6
2 + 5 = 16
Answers
(i) Use the formula for the determinant of a 2×2 matrix.
[tex]\begin{vmatrix}a&b\\c&d\end{vmatrix} = ad-bc[/tex]
[tex]\implies \det(A) = \begin{vmatrix}4 & -3 \\ 2 & 5\end{vmatrix} = 4\times5 - (-3)\times2 = \boxed{26}[/tex]
(ii) The adjugate matrix is the transpose of the cofactor matrix of A. (These days, the "adjoint" of a matrix X is more commonly used to refer to the conjugate transpose of X, which is not the same.)
The cofactor of the (i, j)-th entry of A is the determinant of the matrix you get after deleting the i-th row and j-th column of A, multiplied by [tex](-1)^{i+j}[/tex]. If C is the cofactor matrix of A, then
[tex]C = \begin{pmatrix}5&-2\\3&4\end{pmatrix}[/tex]
Then the adjugate of A is the transpose of C,
[tex]\mathrm{adj}(A) = C^\top = \boxed{\begin{pmatrix}5&3\\-2&4\end{pmatrix}}[/tex]
(iii) The inverse of A is equal to 1/det(A) times the adjugate:
[tex]A^{-1} = \dfrac1{\det(A)} \mathrm{adj}(A) = \boxed{\begin{pmatrix}\frac5{26}&\frac3{26}\\\\-\frac1{13}&\frac2{13}\end{pmatrix}}[/tex]
(iv) The system of equations translates to the matrix equation
[tex]A\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}6\\16\end{pmatrix}[/tex]
Multiplying both sides on the left by the inverse of A gives
[tex]A^{-1}\left(A\begin{pmatrix}x\\y\end{pmatrix}\right)=A^{-1} \begin{pmatrix}6\\16\end{pmatrix}[/tex]
[tex]\left(A^{-1}A\right)\begin{pmatrix}x\\y\end{pmatrix}=A^{-1} \begin{pmatrix}6\\16\end{pmatrix}[/tex]
[tex]\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}\frac5{26}&\frac3{26}\\\\-\frac1{13}&\frac2{13}\end{pmatrix} \begin{pmatrix}6\\16\end{pmatrix}[/tex]
[tex]\begin{pmatrix}x\\y\end{pmatrix}=\boxed{\begin{pmatrix}3\\2\end{pmatrix}}[/tex]
What is the length of AC?
Answers
Answer:
I think it's 5
Step-by-step explanation:
The distance from point A to 0 is 2, then to point B makes it 3, then to point C is a total of 5. Or you could just add the absolute value of A, which is 2, with the absolute value of C, which is 3 to get 5
What is the slope of the line y = x+4?
OA - 12/20
1
OB. 2
O C. -4
OD. 4
Answers
Step-by-step explanation:
Heres the answer And if it doesn't work tell me
Which is an equation of the line that
passes through the points (5,2) and
(10, -3)?
F. y=x-3
G. y=x-8
H. y=-x+7
J. y=-x+12
please help step by step if possible!!
Answers
Step-by-step explanation:
(5,2) & (10,-3)
the slope of the points are
y2 - y1 / x2- x1
-3-2/10-5
-5/5
-1
the mid point of the given points are
x= x1 + x2/2 , y= y1 +y2 /2
.
.
.
.
( , )
the equation of the line that passes through the given points are as
y+ y1 = m (x+ x1)
:. now put the value of the mid point in y1 and x1 and the value of slope in m
also find the mid point, it's hard to do it in a mobile without calculator and paper and pen
sorry
Can someone solve this for me?
Answers
b. i. Use Pythagorus theorem which states that c^2=a^2+b^2
c^2=5^2+7^2
c=8,6
RS=8,61
ii. Use trigonometry(Soh Cah Toa)
sin(50)=5/?
PQ=6,52
iii. a^2=6,52^2-5^2
a=4,18
PL=4,18
PS=4,18+4+7=15,18
PS=15,18
iv. Use the i then Sine rule
c ^2=5 ^2+7 ^2
RS=8,61
sin90/8,61=sinx/5
x=35.5
MSR=35.2
[tex]{x}^{3} {y}^{4} \times {x}^{5} {y}^{ - 5} [/tex]
pls solve this problem
Answers
[tex]x^3 y^4 \cdot x^5 y^{-5}\\\\=x^{5+3} \cdot y^{4-5}~~~~~~~~~~~~~~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\=x^8 y^{-1}\\\\=\dfrac{x^8}{y}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[a^{-n} = \dfrac 1{a^n},~~~ a \neq 0\right][/tex]
20 of my friends play basketball or soccer or both. 8 of them play basketball (and maybe both soccer too), while 5 play both. How many play soccer?
Answers
Answer:
7 frnds will play soccer!
Step-by-step explanation:
8+5 = 13
20 - 13 = 7
I hope it helps u dear! (^^)
Help me pls I don't understand.
Answers
Answer: The correct answer is (-1, 2).
Step-by-step explanation: Find how many units the original F point is away from the center. It is 2 units away in terms of x, and 4 units away in terms of y. The x value has to be negative since the initial x point was already negative. -2/2 = -1. Hence, the x value is -1. 4/2 = 2. Hence, the y value is 2.
what percentage of #1.50 is left after giving out 105k
Answers
Answer:
30%
Step-by-step explanation:
150-105 = 45
(45 / 150 ) * 100 = 30%
The percentage of 150 is left after giving out 105 is 30%
The given numbers are 150 and 105.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Now, the difference of numbers = 150-105=45
45/150 × 100
= 30%
Therefore, the percentage of 150 is left after giving out 105 is 30%
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"Your question is incomplete, probably the complete question/missing part is:"
What percentage of 150 is left after giving out 105.
The image of (-4,-3) reflected across the x-axis is
Answers
Step-by-step explanation:
Reflection in the x axis (x,y)—>(x,-y)
(-4,-3)—>(-4,3)
Chad created a table that shows the ratio of his sports game cards.
Chad’s Cards
Card Type
Outfield
Infield
Catcher
Pitchers
Quantity
3
4
1
2
Next, Chad created the graph below showing possible ratios for Pitchers cards to Infield cards in his deck. Which of the following statements are true?
On a coordinate plane, a graph titled Chad's Cards has Damage on the x-axis and Defense on the y-axis. Points (1, 2), (2, 4), (3, 6), and (4, 8) are plotted.
Chad should not have included the values (1, 2) and (3, 6) because that would mean he only had half a Catcher card.
Chad should not have included the values (1, 2) and (3, 6) because the ratio would be different for these points.
Chad should have changed the axes for the Infield and Pitchers cards so it was the same order as the table.
Chad needs to switch the order of each (x, y) value to show the decreasing values of the Pitchers cards.
Answers
The true statement is on a coordinate plane, a graph titled Chad's Cards has Damage on the x-axis and Defense on the y-axis. Points (1, 2), (2, 4), (3, 6), and (4, 8) are plotted.
Chad created a table that shows the ratio of his sports game cards.
Chad’s Cards
Card Type
Outfield
Infield
Catcher
Pitchers
Quantity
3
4
1
2
Next, Chad created the graph below showing possible ratios for Pitcher cards to Infield cards in his deck.
What is the coordinate plane?
A coordinate plane is a graphing and description system for points and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants in the coordinate plane. The point where these lines connect is called the origin (0, 0).
Therefore the first statement is true,
On a coordinate plane, a graph titled Chad's Cards has Damage on the x-axis and Defense on the y-axis. Points (1, 2), (2, 4), (3, 6), and (4, 8) are plotted.
Therefore option A is correct.
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Answer:
this is right
Step-by-step explanation:
i know it is
Find the perimeter of parallelogram ABCD with vertices A(-5,6), B(2,6), C(1,-2), and D(8,-2)
17 units
43 units
34 units
40 units
Answers
Answer:
34 [units].
Step-by-step explanation:
1) according to the property of parallelogram (AC=BD and AB=CD) the required perimeter can be calculated as P=2AB+2AC;
2) the length of AB=7 (the coordinates 'y' are equal);
3) the length of AC:
[tex]|AC|=\sqrt{(1+5)^2+(-2-6)^2}=10.[/tex]
4) finally, the required perimeter is:
P=2(7+10)=34 [units].
help me thank youuu!
Answers
Answer:
D) 5
Step-by-step explanation:
Because 5x5=25 so the square root would be 5
What is the value of x in this figure?
5√3
10√3
3
о
O 5
o 5√2
O
↓↓
Answers
Check the picture below.
A farmer sells 8.2 kilograms of apples and pears at the farmer's market. 1/4 of this weight is
apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's
Answers
Answer:
6.15 kilograms of pears
Step-by-step explanation:
The total is 8.2 kilograms. Since 1/4 of the weight is apples, we know that 3/4 of the weight is pears. So we multiply 8.2*0.75.
8.2*0.75=6.15
Therefore, the farmer sold 6.15 kilograms of pears at the farmer's market.
Without calculating the cubes find 1 cube+2cube+2(4) cube+(-5)cube+(-6)cube .
Answers
Which of the following points could be the initial point of vector v if it has a
magnitude of 10 and the terminal point (-3,3) ?
(-9,-5)
(-13,-7)
(0,2)
(-0.3,0.3)
Answers
The initial point of vector v if it has a magnitude of 10 and the terminal point (-3,3) is option B (-9,-5).
How to find the vector component?If we have given a vector v of initial point A and terminal point B
v = ai + bj
then the components form as;
AB = xi + yj
Here, xi and yj are the components of the vector.
Given;
The magnitude of 10 and the terminal point (-3,3).
v = ai + bj
v = [tex]\sqrt{a^2 + b^2}[/tex]
10 = [tex]\sqrt{a^2 + b^2}[/tex]
AB = (-3 - a)i + (3 - b)j
If we put (-9,-5)then
AB = (-3 - a)i + (3 - b)j
AB = (-3 + 9)i + (3 + 5)j
AB = 6i + 8j
Put the value in the vector magnitude
10 = [tex]\sqrt{a^2 + b^2}[/tex]
= [tex]\sqrt{6^2 + 8^2}\\\\\sqrt{36+ 64}\\\\\sqrt{100}[/tex]
10 = 10
Thus, The correct option is B (-9,-5).
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Fabian took a taxi from his house to the airport. The taxi company charged a pick-up fee of $4.80 plus $4 per mile. The total fare was $44.80, not including the tip. How many miles was the taxi ride?
Answers
Answer:
Answer = 10 miles
Step-by-step explanation:
First lets make an equation we know that the pick up fee was $4.80 and that Fabian had to pay an extra $4 for every mile. The total amount Fabian paid was $44.80. So the equation would look like this, 4x+4.80=44.80. When we solve for x we find that the taxi ride was 10 miles.
Hope that helps! :)
The taxi ride was 10 miles long. Fabian traveled 10 miles from his house to the airport.
To calculate the distance of Fabian's taxi ride, let's denote the distance in miles as "d." The cost consists of a pick-up fee of $4.80 and a mileage charge of $4 per mile. So, the total cost can be represented as 4.80 + 4d. Given that the total fare was $44.80, we can set up the equation:
4.80 + 4d = 44.80
Now, solving for "d," subtract 4.80 from both sides:
4d = 40
Divide both sides by 4:
d = 10
Therefore, the taxi ride was 10 miles long. Fabian traveled 10 miles from his house to the airport.
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Need an answer whoever can do it thank youuu!!!!
Answers
Answer:
65.3ft
Step-by-step explanation:
I think it might be this I'm not sure
help with this math
Answers
Based on the figures given, and the line graph, we can tell that the months with the greatest change in average low temperature were May and July.
Which months saw the greatest changes in temperature?In the month of May, the temperature changed by:
= 60 - 51
= 9°F
In the month of July, the temperature changed by:
= 66 - 62
= 4°F
These two months therefore saw the largest changes in temperature and this is confirmed by the line graph.
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SOMEONE HELP ASAP! PLEASE EXPLAIN IN DEPTH!
Find the area. You must show all work to receive credit. (10 points)
Figure ABCDEF is shown. A is located at negative 5, negative 8. B is located at 1, negative 8. C is located at 3, negative 5. D
Answers
The area of the figure is 51.4 unit²
The complete questionFigure ABCDEF is shown. A is located at 5, negative 8. B is located at 11, negative 8. C is located at 11, 0. D is located at 6
See attachment for the figure
The area of the figureThe figure can be divided into the following shapes:
Trapezoid 1: Opposite sides = (8 and 5) and height = 5Trapezoid 2: Opposite sides = (5 and 4.8) and height = 2Triangle: Base = 4.8 and height = 4The area of the trapezoid is:
Area = 0.5 * (Sum of opposite sides) * height
So, we have:
Trapezoid 1 = 0.5 * (8 + 5) * 5 = 32.5
Trapezoid 2 = 0.5 * (5 + 4.8) * 2 = 9.8
The area of the triangle is:
Area = 0.5 * Base * Height
This gives
Triangle = 0.5 * 4.8 * 4 = 9.6
Add the individual areas
Area = 32 + 9.8 + 9.6
Evaluate the sum
Area = 51.4
Hence, the area of the figure is 51.4 unit²
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Kelsey has a new baby brother!
He weighs 8 lbs 3 oz. The
doctor said the baby should
gain about 5 ounces per week.
At that rate, how much should
the baby weigh in 3 months (12
weeks)? In lb and oz
Answers
5 ounces per week x 12 weeks = 60 ounces
1 pound = 16 ounces
60 / 16 = 3 pounds 12 ounces
3 pounds 12 ounces + 8 pounds 3 ounces = 11 pounds 15 ounces
answer: 11 pounds 15 ounces
The population standard deviation for the height of college hockey players is 3.4 inches. If we want to estimate 90% confidence interval for the population mean height of these players with a 0.6 margin of error, how many randomly selected players must be surveyed? (Round up your answer to nearest whole number) Answer:
Answers
Answer:
i thank 4 for this players
What 3- D figure does the net below create when folded?
Answers
The net given below when folded will form a 3-Dimensional shape, this shape is a triangular prism.
What is a triangular prism?Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.
Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.
The net given below when folded will form a 3-Dimensional shape, this shape is a triangular prism.
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Which number line shows the solution to the inequality 3x + 3 ≥ 12?
Answers
Answer:
3x+3 ≥ 12
3x ≥ 9
x ≥ 3
So A is correct
Let me know if this helps or if you have any other questions!